Back in ye olden days they very much were a pet class. Though realistically outside of solo play, or very niche interrupt settings, a warlock not running their imp was an idiot.
Todays pets are, generally speaking, useless trash in many ways. Voidwalker barely holds threat, and more often than not just outright fails. Succubus does the best damage, but has the worst ability. Imp does decent damage, has a self purge, but in this age of constant movement is often way out in the middle of the boonies since you’ve had to move so far away due to mechanics. It, thankfully, has a ‘pull to caster’ ability, but that I believe takes a GCD to use.
Felhunter is the one most warlocks will use if forced. It’s damage is worse than Succubus, about on par with imp, and the less we consider the VW on this the better. It’s utility however is situationally amazing to the best thing ever with a kick ability, and the purge can be a godsend if you remember to use it.
Felguard is just outright amazing in comparison to the rest. Doesn’t have a taunt like the VW, but holds threat on ST and MT way better. Far more tankier than the rest, and I’m not certain the VW actually holds up to them in that regard either. Damage just from auto-attack is easily double the output of the Succubus.
However, there is nothing special about pets in general. Hunters have more cosmetic choices in that they can literally tame anything that appeals to them, even if they will effectively play the same as any other pet in their category (Cunning, ect). Talent amps are fairly lack luster for our pets too, the best being the Synergy ability so when it procs you get a damage increase. It works the same in reverse, but with their damage already garbage its barely noticeable, and only if you really look for it. Felguard not withstanding, of course.
Is the Warlock a pet class? Given Blizzard justified it’s recent nerf on a thematic understanding of such, then it is not. The Warlock is a Slaver; We don’t form bonds with our pets like Hunters do, we dominate them, make them dance to our will or die for our pleasure. That’s the thematic truth of Warlocks when it comes to being a ‘pet’ class IMO.